The Fate of Supersymmetry in Quantum Field Theories

We analyze the significance of supersymmetry in two topological models and the standard model (SM). We conclude that the two topological field theory models favor hidden supersymmetry. The SM superpartners, instead, have not been found.

Supersymmetry in the Geometric Representation of the Early Universe Wave Function

The main goal of this article is to present a new result of a possible approach to the geometrical description of the birth and evolution of the universe. The novelty of the article is that it is possible to explain the nature of supersymmetry in terms of the geometric representation of the wave function and to propose a mechanism of spontaneous symmetry breaking of the excitation of the universe with different degrees of freedom. It is under such conditions that the well-known spontaneous symmetry breaking occurs and individual excitation acquires mass. At the same time, a phase transition of the first kind occurs with the formation of a new phase.

Path Integral Quantization of Superparticle with 1/4 Supersymmetry Breaking

We present path integral quantization of a massive superparticle in d =4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N = 8 to N = 2. Its worldline action contains a Wess-Zumino term, explicitly breaks d =4 Lorentz symmetry and exhibits one complex fermionic k-symmetry. We perform the Hamilton-Jacobi formalism of constrained systems, to obtain the equations of motion of the model as total differential equations in many variables. These equations of motion are in exact agreement with those obtained by Dirac’s method.

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.

Darboux Transformation in Quantum Black-Scholes Hamiltonian and Supersymmetry

In this paper, we consider the Black-Scholes (BS) equation for option pricing with constant volatility. Here, we construct the first-order Darboux transformation and the real valued condition of transformed potential for BS corresponding equation. In that case we also obtain the transformed of potential and wave function. Finally, we discuss the factorization method and investigate the supersymmetry aspect of such corresponding equation. Also we show that the first order equation is satisfied by commutative algebra.

On Supersymmetry and the Origin of Dark Matter

Dark matter was first suspected in clusters of galaxies when these galaxies were found to move with too high a speed to be retained in the cluster by their gravitational influence on each other. Some current theories favor cold dark matter models where particles are created with low velocity dispersions and thus would become trapped in baryonic gravitational potentials. According to the standard Big-Bang model, dark matter is of nonbaryonic origin, otherwise the observed abundance of helium in the Universe would be violated. In this work, recent theoretical and observational developments are used to form a consistent picture of the events in the early Universe that gave rise to dark matter. According to the model that will be presented in this paper, supersymmetry plays a major role. In addition, the possibility that dark matter evolves in a spacetime manifold different from that of the observed Universe is discussed.

Towards 6D Little String Theory of Particles

A model for particles based on preons in chiral, vector and tensor/graviton supermultiplets of unbroken global supersymmetry is engineered. The framework of the model is little string theory. Phenomenological predictions are discussed.

Stringy Phenomenology with Preon Models

We compare, following Pati, global symmetries, our topological supersymmetric preon model with the heterotic E8 × E8 string theory. We include Pati’s supergravity based preon model in this work and compare the preon interactions of his model to ours. Based on preon-string symmetry comparison and preon phenomenological results, we conclude that the fundamental particles are likely preons rather than standard model particles. .

Perspectives on Higgs boson and supersymmetry

We review the recent discovery of the Higgs like particle at - 125 GeV and its implications for par- ticle physics models. Specifically the implications of the relatively high Higgs mass for the discovery of supersymmetry are discussed. Several related topics such as naturalness and supersymmetry, dark matter and unification are also discussed.

Lepton flavor violating Z-boson decays at GigaZ as a probe of supersymmetry

This paper briefly reviews the lepton flavor violating Z-decays at GigaZ as a probe of supersymmetry by focusing on Z → i j in two representative supersymmetric models: the minimal supersymmetric model without R-parity and the supersymmetric seesaw model.The work concludes that under the current experimental constraints from LEP and i → j γ,these rare decays can still be enhanced to reach the sensitivity of the GigaZ.Therefore,supersymmetry can be probed via these decays at GigaZ.

b→cτ■ decay in supersymmetry with R-parity violation

In past years, several hints of lepton flavor universality (LFU) violation have emerged from the b→sl^+l^-and data. More recently, the Belle Collaboration has reported the first measurement of the D^* longitudinal polarization fraction in the B→D^*τν decay. Motivated by this intriguing result, along with the recent measurements of and polarization, we present the study of b→cτν decays in supersymmetry (SUSY) with -parity violation (RPV). We consider B→D^(*)τν, Bc→ηcτν, Bc→J/ψτν and modes and focus on the branching ratios, LFU ratios, forward-backward asymmetries, polarizations of daughter hadrons, and the lepton. The RPV SUSY was capable of explaining the RD^(*)anomalies at the 2σ level, after taking into account various flavor constraints. In the allowed parameter space, the differential branching fractions and LFU ratios are largely enhanced by the SUSY effects, especially in the large dilepton invariant mass region. Moreover, a lower bound 10^-6 is obtained. These observables could provide testable signatures at the high-luminosity LHC and SuperKEKB, and correlate with direct searches for SUSY.

SEARCHES FOR MONOPOLES, SUPERSYMMETRY, TECHNICOLOR, COMPOSITENESS, EXTRA DIMENSIONS, etc.

Magnetic Monopole SearchesIsolated supermassive monopole candidate events have not been confirmed. The most sensitive experiments obtain negative results.

Analysis of B_s→Φμ^+μ^- decay within supersymmetry

Motivated by the first measurement on B（Bs→ Ф μ^＋ μ^-by the CDF Collaboration, we study the supersymmetric effects in semi-leptonic Bs→ Ф μ^＋ μ^-ecay. In our evaluations, we analyze the dependences of the dimuon invariant mass spectrum and the forward-backward asymmetry on relevant supersymmetric couplings in the MSSM with and without R-parity. The analyses show that the new experimental upper limits of B（Bs→ Ф μ^＋ μ^-from the LHCb Collaboration could further improve the bounds on sneutrino exchange couplings and （δ^u LL）23 as well as （δ^d LL,RR）23 mass insertion couplings. In addition, within the allowed ranges of relevant couplings under the constraints from B（Bs→ Ф μ^＋ μ^- B（B → K^（＊） μ^＋ μ^-and B（Bs → μ^＋ μ^-, the dimuon forward-backward asymmetry and the differential dimuon forward-backward asymmetry of Bs→Ф μ^＋ μ^-re highly sensitive to the squark exchange contribution and the （ LL）23 mass insertion contribution. The results obtained in this work will be very useful in searching for supersymmetric signals at the LHC.

A new kind of graded Lie algebra and parastatistical supersymmetry

In this paper the usual Z2 graded Lie algebra is generalized to a new form, which may be called Z2,2 graded Lie algebra. It is shown that there exist close connections between the Z2,2 graded Lie algebra and parastatistics, so the Z2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems.

Supersymmetry and the Dirac Equation with Vector and Scalar Coupling Potentials

This paper shows that one type of first order Dirac equation with vector coupling and scalar coupling potentials can be brought into the framework of non relativistic supersymmetric quantum mechanics. The conclusion is independent of the concrete forms of the vector and scalar coupling potentials because of the nilpotent matrix realization of supersymmetric quantum mechanical algebra. The supersymmetry of this kind of Dirac equation requires that a spin orbit coupling term be introduced into the associated supersymmetric Hamiltonian.

A new(2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new （2＋1）-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known （2＋1）-dimensional negative Kadomtsev-Petviashvili equation but also the extension of the known （1＋1）-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac-Moody-Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.

Bosonization Approach and Novel Traveling Wave Solutions of the Superfield Gardner Equation

In this paper, the bosonization of the superfield Gardner equation in the case of multifermionic parameters is presented and novel traveling wave solutions are extracted from the coupled bosonic equations by using the mapping and deformation relations. In the case of two-fermionic-parameter bosonization procedure, we provide a special solution in the form of Jacobian elliptic functions. Meanwhile, we discuss and formally derive traveling wave solutions of N fermionic parameters bosonization procedure. This technique can also be applied to treat the N = 1 supersymmetry KdV and mKdV systems which are obtained in two limiting cases.

I-Theory: A Unifying Quantum Theory?

This paper gives an overview of a new theory called the “I-Theory”, in the context of several accepted theories in physics and cosmology. This paper reviews the salient features of the “I-Theory”, which introduces new particles like I, S∞ and A1 particles and provides a fuller understanding about Dark Matter, Dark Energy, Matter/Anti Matter and the four fundamental forces. “I-Theory” introduces a new concept of the “quality” of energy with White, Black and Red matter formed with regard to the frequency level of the energy vibration. The authors discuss the main features and controversies of the Standard Model, General Relativity, Big Bang, and Supersymmetry and attempt to answer some of the unsolved questions. It is proposed that the “I-Theory” can successfully encompass all major theories and thereby becomes the theory of the whole, the Unifying Theory.

Revealing the Ubiquitous Effects of Quantum Entanglement—Toward a Notion of God Logic

Following Spinoza-Einstein’s interpretation of God or nature, the notion “God Logic” is proposed. This notion is to serve as an elicitation for a consistent set of necessary criteria for: 1) developing the logical foundation of quantum gravity as envisaged by Einstein, 2) revealing the ubiquitous effects of quantum entanglement as suggested by Roger Penrose, and 3) programming the universe as proposed by Seth Lloyd. An evolving set of eleven criteria is proposed for the notion. The possibility of inventing such a logical system is analyzed. A supersymmetrical candidate logic of negative-positive energy dynamic equilibrium is introduced and assessed against the set of criteria. It is shown that the first 10 criteria are met or partially met by the candidate. But the question whether the 11th criterion has been or can be met is left open for discussion and further research effort. The assessment leads to a few predictions. Notably, it is predicted that, should Boson-Fermion symmetry or broken symmetry be observed, it would be caused by bipolar symmetry or broken symmetry of negative-positive energies.

N ＝ 4 Superconformal Quantum Mechanics in One Dimension and Its Algebraic Structure

N = 4 superconformal quantum mechanics of nonrelativistic particles in the typical 1/x2-potentials, which holds not only supersymmetry but also dynamical conformal symmetry, is studied. The corresponding superconformal quantum mechanical algebra, which contains supersymmetric quantum mechanical algebra with four supercharges and conformal algebra as subalgebras, and its two canonical group chains are established.